Base units for resistance and how would I work it out?

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JaredzzC
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I couldn't for the life of me work this out.

I was given 4 choices:

A) kgms-2
B) kgm2 s-1
C) kgm2 A-1 s-1
D) kgm2 A-2 s-3

After searching online, I came across the answer being D, with the explanation of Ohm = volt/amp = m2 kg / sec3 A2

What I don't understand is how, in an exam situation, I would go about trying to answer it?

I don't believe either in the revision guide or text book it mentions the base units for either volt or amp and the definition of them (whether worded or as an equation) doesn't seem to help me figure out their base units, so how would I be able to work out what they were?
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uberteknik
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(Original post by JaredzzC)
I couldn't for the life of me work this out.

I was given 4 choices:

A) kgms-2
B) kgm2 s-1
C) kgm2 A-1 s-1
D) kgm2 A-2 s-3

After searching online, I came across the answer being D, with the explanation of Ohm = volt/amp = m2 kg / sec3 A2

What I don't understand is how, in an exam situation, I would go about trying to answer it?

I don't believe either in the revision guide or text book it mentions the base units for either volt or amp and the definition of them (whether worded or as an equation) doesn't seem to help me figure out their base units, so how would I be able to work out what they were?

By using a combination of definitions and reducing them to the fundamental base SI units.

Start with ohms law:

R = V/I

Current has the SI base unit of Amperes so this cannot be reduced any further.

R = VA-1

Voltage = Joules per Coulomb of charge

V = JC-1

Joules and Coulombs are derived so need to be broken down further.

Q = It = Ampere seconds = As

Both Amperes and seconds are SI base units and cannot be reduced further.

Joules = Energy = mc2 = Kg (m s-1)2 = Kg m2 s-2

Kg, m and s are all SI base units.


Having reduced all of the definitions to SI base units all that's left is putting it all back together:

R = V/I = JC-1A-1

substituting

R = Kg m2 s-2 (A s)-1 A-1

removing brackets

R = Kg m2 s-2 A-1 s-1 A-1

collecting like terms:

R = Kg m2 s-3 A-2

Voila!
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JaredzzC
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(Original post by uberteknik)
By using a combination of definitions and reducing them to the fundamental base SI units.

Start with ohms law:

R = V/I

Current has the SI base unit of Amperes so this cannot be reduced any further.

R = VA-1

Voltage = Joules per Coulomb of charge

V = JC-1

Joules and Coulombs are derived so need to be broken down further.

Q = It = Ampere seconds = As

Joules = Energy = mc2 = Kg (m s-1)2 = Kg m2 s-2

Putting it all back together

R = V/I = JC-1A-1

substituting

R = Kg m2 s-2 (A s)-1 A-1

removing brackets

R = Kg m2 s-2 A-1 s-1 A-1

reducing

R = Kg m2 s-3 A-2

Viola.
Wow, thank you so much! That was incredibly helpful and I was able to understand and follow it quite clearly. The best explanation I have come across.

This worries me a little though as this was part of the multiple choice section of questions, so it was worth only 1 mark for the answer. Seems a little long-winded for such a mark which leads me to believe that perhaps we are meant to know this, as oppose to work it out (but that wouldn't really make logical sense because just by knowing it we aren't able to determine how to derive it and hence understand it).
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uberteknik
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(Original post by JaredzzC)
Wow, thank you so much! That was incredibly helpful and I was able to understand and follow it quite clearly. The best explanation I have come across.

This worries me a little though as this was part of the multiple choice section of questions, so it was worth only 1 mark for the answer. Seems a little long-winded for such a mark which leads me to believe that perhaps we are meant to know this, as oppose to work it out (but that wouldn't really make logical sense because just by knowing it we aren't able to determine how to derive it and hence understand it).
You are welcome.

I derived it from first principles to explain how to apply it to any physical definition.

During the examination, multiple choice answers can often be eliminated by inspection.

In this question, we know that R = V/I so Amperes must appear in the units somewhere. That immediately eliminates a) and b).

Voltage is Joules per coulomb of charge and since charge = It, amperes appears twice which logically excludes c).

Sometimes it's as simple as that. After all it is only one mark.
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